Railgun's are ok. Their real selling point is that they can be used for long distance engagements where missiles are impractical due to slow speeds and can be avoided at range. Even the accelerated missile launcher is a little slow after about 300 meters. small rails need a damage boost

I agree. They should be a viable long range AV option. They already have the long range going for them, but the dps really leaves a lot to be desired.
I disagree about them rocking the target though. Explosives have that ability for obvious reasons, that railguns don't have. Plus, the relative inability to dodge rail shots would turn dropship journeys into pinball.

As part of an Anti-Aircraft experiment, I fitted an LAV with a light railgun this weekend (standard, and with hybrid turret operation at II before people start talking about using militia)

First, I would like to say that it takes a good deal of practice to even HIT a dropship with one of these things, but that isn't really the problem.

The problem is, when it does hit, it doesn't even phase the dropship.
As of right now, light railguns do slightly more damage than light missile launchers- about 300 for standards- thats about the same as a standard swarm launcher. Except, unlike swarm launchers and small missile turrets, light railguns have to be charged up, have a tiny blast radius and next to no splash damage, and don't shake up dropships like missiles do.

Why exactly is an AV-specific weapon, which has to be mounted on a vehicle, less effective than infantry-held weapons and turrets meant for a generalist use?

I believe that light railguns need a slight damage boost- at least by 50.

at least by 100 in my opinion

If that works, great. But I think 100 may be a bit much. 50 is just enough to give them a noticeable advantage over missiles.

at least by 100 in my opinion

Blasters also need more love